P.A. Cox - Inorganic chemistry (793955), страница 29
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These trends are sometimeserroneously ascribed to ‘lattice packing’ effects, with the implication that two large ions together have a larger latticeenergy than a large and a small ion. Theoretical (and experimental) estimates of lattice energies contradict this view,and a satisfactory explanation depends on a balance of energies (see also Topic E4).Consider the decomposition of a group 2 metal carbonate MCO3:Figure 2 shows a thermochemical cycle, which predicts that the enthalpy change in this reaction is(2)where X is enthalpy input required for the gas-phase decomposition ofand HL are the lattice enthalpies.
X ispositive, but according to Equation 1 the lattice energy of MO will always be larger than that of MCO3 because theoxide ion is smaller. The difference of lattice energies in Equation 2 therefore gives a negative contribution to theoverall ΔH. If we have a larger M2+ ion, both lattice energies become smaller, but the important thing is that theirdifference becomes smaller. Thus smaller M2+ gives a less endothermic decomposition reaction, which is thereforepossible at a lower temperature.SECTION D—STRUCTURE AND BONDING IN SOLIDSFig. 2. Thermochemical cycle for the decomposition of MCO3.123Section D—Structure and bonding in solidsD7ELECTRICAL AND OPTICAL PROPERTIES OF SOLIDSKey NotesThe band modelBandgapsDielectric propertiesInfluence of defectsRelated topicMetallic solids have a continuous band of electronic energy levels withthe top filled level, the Fermi level, within it.
In nonmetallic solids thereis a bandgap separating the filled valence band from the empty conductionband.Bandgaps determine the optical absorption of a nonmetallic solid and thepossibility of semiconduction. Bandgaps in binary solids decrease withdecreasing electronegativity difference between the elements. In mostionic and covalent solids bandgaps are smaller with elements in lowerperiods.The static dielectric constant of a solid arises from the displacement ofions in an electric field and may be particularly large for some ionic solids.The high-frequency dielectric constant depends on electronicpolarizability and determines the optical refractive index.Defects including impurities have a major influence on the electricalproperties of nonmetallic solids. They can provide extra electrons orholes, which enhance semiconduction, and they can also facilitateconduction by ions.Element structures (D2)The band modelThe band model of solids is an extension of the molecular orbital (MO) method (see Topics C4–C7).
The overlap ofatomic orbitals in an extended solid gives rise to continuous bands of electronic energy levels associated with differentdegrees of bonding. In a simple monatomic solid the bottom of the band is made up of orbitals bonding between allneighboring atoms; orbitals at the top of the band are antibonding, and levels in the middle have an intermediatebonding character.
Different atomic orbitals can, in principle, give rise to different bands, although they may overlap inenergy.The fundamental distinction between metallic and nonmetallic solids arises from the way in which orbitals arefilled (see Fig. 1). Metallic behavior results from a band partially occupied by electrons, so that there is no energy gapbetween the top filled level (known as the Fermi level) and the lowest empty one.
On the other hand, a nonmetallicsolid has a bandgap between a completely filled band (the valence band VB) and a completely empty one (theconduction band CB). In a filled band the motion of any electron is matched by another one moving in the oppositedirection, so that there is no net motion of electric charge. For conduction to occur in a nonmetallic solid, therefore,some electrons must be excited from the VB to the CB. This gives rise to an activation energy, and conductivitySECTION D—STRUCTURE AND BONDING IN SOLIDS125Fig. 1. Band picture for (a) nonmetallic and (b) metallic solid; occupied electronic levels are shown shaded.increases with rise in temperature approximately in accordance with the Arrhenius equation used in chemicalkinetics (see Topic B3).Nonmetallic solids include ionic and covalent compounds.
In the former case, the VB is made up of the top filledanion levels (e.g. the 3p orbitals of Cl−, which are filled in making the ion) and the CB of the lowest empty cation levels(e.g. in Na+ the 3s level from which an electron has been removed to make the cation). In covalent solids such asdiamond the VB consists of bonding orbitals (e.g.
C—C) and the CB of antibonding orbitals.Simple metallic solids are elements or alloys with close-packed structures where the large number of interatomicoverlaps gives rise to wide bands with no gaps between levels from different atomic orbitals. Metallic properties canarise, however, in other contexts. In transition metal compounds a partially occupied d shell can give rise to a partlyfilled band. Thus rhenium in ReO3 has the formal electron configuration 5d1 (see Topic H1) and is metallic.
WO3 (formally5d0) is not metallic but Na0.7WO3 is, as electrons from sodium occupy the band made up of W 5d orbitals (seeTopic D5).BandgapsThe bandgap in a nonmetallic solid is important for electrical and optical properties. A solid with a small bandgap is asemiconductor with a conductivity that (unlike the case with a metal) increases as temperature is raised. The bandgapalso determines the minimum photon energy required to excite an electron from the VB to the CB, and hence thethreshold for optical absorption by a solid.In a covalent solid the bandgap is related to the energy splitting between bonding and antibonding orbitals (seeTopic C4) and thus to the strength of bonding.
In an ionic solid the bandgap is determined by the energy required totransfer an electron back from the anion to cation, which is related to the lattice energy (see Topic D6). Bandgaps forelements and binary compounds follow some systematic trends.• In a series of isoelectronic solids such as CuBr-ZnSe-GaAs-Ge the bandgap decreases with decreasingelectronegativity difference between the two elements. This trend reflects the decreasing energy difference between‘anion’ and ‘cation’ orbitals.• In series such as C-Si-Ge or LiF-NaF-KF the bandgap decreases as the group is descended and atoms or ions becomelarger. This trend reflects the decline in bond or lattice energies with larger atoms or ions (see Topics C8 and D6).A comparison between compounds of pre-transition metals (e.g.
Ca) and corresponding post-transition metals (e.g.Cd) provides a good example of the influence of the electronegativity differences (see Topic G1). Bandgaps are smaller126D7—ELECTRICAL AND OPTICAL PROPERTIES OF SOLIDSin compounds of the less electropositive post-transition metals. The colors of CdS and CdSe (used as yellow and redpigments) come from strong absorption of blue light, as the bandgaps correspond to photon energies in the visiblespectrum. Analogous calcium compounds are not colored as the larger bandgaps correspond to UV radiation.Dielectric propertiesThe dielectric constant of a medium is a measure of the electrostatic polarization, which reduces the forces betweencharges (see Topics C10 and E1 for liquids). Two different mechanisms contribute to the dielectric properties of a solidaccording to the time-scale involved.
The static dielectric constant depends on the displacement of ions from theirregular positions in an applied electric field. It is applicable for static fields, or frequencies of electromagnetic radiationup into the microwave range. The high-frequency dielectric constant is measured at frequencies faster than thevibrational motion of ions.
It is applicable in the visible region of the spectrum, and determines the refractive index,which governs the transmission of light in transparent media.As expected, ionic substances have higher static dielectric constants than nonionic ones. Especially large values arisewhen ions can be easily displaced from their positions in the regular structure.
For example, barium titanate BaTiO3 hasa very high dielectric constant that varies with temperature. In the perovksite structure (see Topic D5) the large Ba2+ion imposes a relatively large O—O distance so that Ti4+ can move easily out of the center of its octahedral site. Below120°C a permanent distortion sets in, which gives each unit cell a dipole moment. This type of behavior is calledferroelectric and has important applications, for example, in capacitors for electronic circuits.Large high-frequency dielectric constants (and hence refractive indices) depend not on ionic motion but on electronicpolarizability. Large ions contribute to this, and glasses containing Pb2+ are traditionally used for lenses where a highrefractive index is necessary. Electronic polarizability can also be large in compounds with small bandgaps.
A gapoutside the visible spectrum is necessary for a colorless material in optical applications. TiO2 is used as a white pigmentbecause it has the right optical properties combined with cheapness, chemical stability and non-toxicity. The bandgap isonly just in the UV, and the refractive index in the visible spectrum is high. Each grain is highly reflective, and apowdered sample appears white because light is reflected in random directions.Influence of defectsAll solids contain defects where the regularity of the ideal periodic lattice is broken.
Line and plane defects(dislocations, grain boundaries, etc.) are important for mechanical properties but it is point defects that are mostsignificant for electrical properties. They include• vacancies or atoms missing from regular lattice positions;• interstitials or atoms in positions not normally occupied;• impurities either accidentally present or introduced as deliberate doping.Defects that introduce extra electrons, or that give missing electrons or ‘holes’, have a large influence on electronicconduction in nonmetallic solids. Most semiconductor devices use doped or extrinsic semiconductors rather thanthe intrinsic semiconduction of the pure material. Doping Si with P replaces some tetrahedrally bonded Si atoms in thediamond lattice (see Topic D2) with P.
Each replacement provides one extra valence electron, which requires only asmall energy to escape into the CB of silicon. This is an n-type semiconductor. On the other hand, replacing an Si atomwith Al gives a missing electron or ‘hole’, which may move in the VB giving a p-type semiconductor. Some othertypes of nonmetallic solid can be doped, especially compounds of transition metals, which have variable oxidationSECTION D—STRUCTURE AND BONDING IN SOLIDS127states.
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